Problem: Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{y^2 + 4y - 5}{y^2 - y}$
First factor the expressions in the numerator and denominator. $ \dfrac{y^2 + 4y - 5}{y^2 - y} = \dfrac{(y + 5)(y - 1)}{(y)(y - 1)} $ Notice that the term $(y - 1)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(y - 1)$ gives: $n = \dfrac{y + 5}{y}$ Since we divided by $(y - 1)$, $y \neq 1$. $n = \dfrac{y + 5}{y}; \space y \neq 1$